In a class of 60 students, 40 students play cricket and only 30 students play football . The number of students who can play both cricket and football is

Options

A. 10
B. 23
C. 33
D. 34

Answer

To solve the problem step by step, we can use the principle of set theory. Let's denote:

- \( C \): the set of students who play cricket
- \( F \): the set of students who play football

Given:
- Total number of students, \( n = 60 \)
- Number of students who play cricket, \( |C| = 40 \)
- Number of students who play football, \( |F| = 30 \)

We need to find the number of students who play both sports, denoted as \( |C \cap F| \).

### Step 1: Use the formula for the union of two sets
The formula for the union of two sets is given by:

\[ |C \cup F| = |C| + |F| - |C \cap F| \]

Where:
- \( |C \cup F| \) is the total number of students who play at least one of the sports (which is 60 in this case).

### Step 2: Substitute the known values into the formula
We substitute the known values into the formula:

\[ 60 = 40 + 30 - |C \cap F| \]

### Step 3: Simplify the equation
Now, simplify the equation:

\[ 60 = 70 - |C \cap F| \]

### Step 4: Solve for \( |C \cap F| \)
Rearranging the equation gives:

\[ |C \cap F| = 70 - 60 \]

\[ |C \cap F| = 10 \]

### Conclusion
Thus, the number of students who can play both cricket and football is \( 10 \).